A can do $$\frac{2}{5}$$ of a work in 6 days and B can do $$\frac{2}{3}$$ of the same work in 12 days. A and B worked together for 6 days. C alone completed the remaining work in 8 days. A and C, working together, will complete the same work in:

A can-do $$\dfrac {2}{3}$$ work in days 

A complete work in  $$\dfrac {6}{2} \times 5 = 15 days $$ 

B can do $$\dfrac {2}{3}$$ work in 12 days 

B complete work in  $$ \dfrac {12}{2}\times 3 = 18 days $$

1 day work of A and B = $$ \dfrac {1}{15}+\dfrac {1}{18}$$

$$\Rightarrow \dfrac {6+5}{90} = \dfrac {11}{90 } units$$

Remaining work = $$ 1 \dfrac {11}{90}\times 6 = \dfrac {24}{90} = \dfrac {4}{15}$$

This work is completed by C in 8 days 

1 day work of C = $$ \dfrac {4}{15} \times 8 = \dfrac {1}{30}$$ units

1 day work of A and C = $$ \dfrac {1}{15} + \dfrac {1}{30} = \dfrac {2+1}{30} = \dfrac {1}{10}$$ units

Time taken by A and C to complete work = 10 days